Tikhonov regularized solutions for improvement of signal-to-noise ratio in case of auditory-evoked potentials

Abstract

In the present study, standard Tikhonov regularization (STR) Technique and the subspace regularization (SR) method have been applied to remove the additive EEG noise on average auditory-evoked potential (EP) signals. In methodological manner, the difference between these methods is the formation of regularization matrices which are used to solve the weighted problem of EP estimation. Those methods are compared to ensemble averaging (EA) with respect to signal-to-noise-ratio (SNR) improvement in experimental studies, simulations and pseudo-simulations. The results of tests no superiority of the SR in comparison to STR has been observed. In addition, the STR is found to be less computational complex. Moreover, results support the theoretical fact that the STR was introduced to be optimum for smooth solutions whereas the SR allows sharp variations in solutions. Thus, the STR is found to be more useful in removing the noise with the average signal remaining.